1,192 research outputs found
Completeness of mutiseparable superintegrability in E2, C
No full textKalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.. (1999). Completeness of mutiseparable superintegrability in E2, C. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3408
Completeness of multiseparable superintegrability on the complex 2-sphere
No full textKalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.. (1999). Completeness of multiseparable superintegrability on the complex 2-sphere. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3424
Contractions of Lie algebras: Applications to special functions and separation of variables
No full textKalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.. (1999). Contractions of Lie algebras: Applications to special functions and separation of variables. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3319
Superintegrability on the two dimensional hyperboloid II
No full textKalnins, E.G.; Miller, Jr., W.; Hakobyan, Ye.M.; Pogosyan, G.S.. (1998). Superintegrability on the two dimensional hyperboloid II. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3273
On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space
No full textKalnins, E.G.; Williams, G.C.; Miller, Jr., W.; Pogosyan, G.S.. (2002). On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3761
Models for Quadratic Algebras Associated with Second Order Superintegrable Systems in 2D
No full textThere are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible representations of the quantum quadratic algebras though the construction of models in which the symmetries act on spaces of functions of a single complex variable via either differential operators or difference operators. In another paper we have already carried out parts of this analysis for the generic nondegenerate superintegrable system on the complex 2-sphere. Here we carry it out for a degenerate superintegrable system on the 2-sphere. We point out the connection between our results and a position dependent mass Hamiltonian studied by Quesne. We also show how to derive simple models of the classical quadratic algebras for superintegrable systems and then obtain the quantum models from the classical models, even though the classical and quantum quadratic algebras are distinct
Lie algebra contractions on two-dimensional hyperboloid
No full textThe In�n�-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the four corresponding two-dimensional homogeneous spaces: two-dimensional hyperboloids and two-dimensional Euclidean and pseudo-Euclidean spaces. We show how the nine systems of coordinates on the two-dimensional hyperboloids contracted to the four systems of coordinates on E2 and eight on E1,1. The text was submitted by the authors in English. � 2010 Pleiades Publishing, Ltd
Lie-algebra contractions and separation of variables. Three-dimensional sphere
No full textThe Inönü-Wigner contraction from the SO(4) group to the Euclidean E(3) group is used to relate the separation of variables in Helmholtz equations for two corresponding homogeneous spaces. We show how the six systems of coordinates on the three-dimensional sphere contracted to nine systems of coordinates on Euclidean space. As a consequence of the Inönü-Wigner contraction we also consider contractions of the integrals of motion. 2009 Pleiades Publishing, Ltd
Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials
No full textThe structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results for the strictly 1-parameter case have been incomplete. Here we work out this structure theory and prove that the quadratic algebra generated by first and second order constants of the motion for systems with 4 second order constants of the motion must close at order three with the functional relationship between the 4 generators of order four. We also show that every 1-parameter superintegrable system is Stäckel equivalent to a system on a constant curvature space
The Kepler-Coulomb problem on SO(2, 2) hyperboloid
No full textIn this note the Kepler-Coulomb problem in hyperbolic space H2 2: z0 2 + z1 2 - z2 2 - z3 2 = R2 is discussed. � 2012 Pleiades Publishing, Ltd
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